A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts.

4, 9, 6, 9, 36, 11, 14, 81, 16, 19, 30, 15, 24, 225, 26, 19, 48, 31, 34, 441, 36, 39, 84, 35, 44, 69, 32, 49, 900, 51, 34, 87, 56, 59, 1296, 61, 40, 141, 66, 69, 108, 49, 74, 159, 64, 53, 126, 81, 84, 2601, 86, 89, 2916, 91, 94, 147, 66, 61, 66, 101, 70, 165

Offset

2,1

Comments

A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).

A nontrivial cevian is one that does not coincide with a side of the triangle.

For all n, the longest nontrivial integral cevian has length n^2.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Wikipedia, Cevian

Wikipedia, Isosceles triangle

Example

a(4) = 6 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.

Prog

(PARI)
ceviso(n) = {
  my(d, L=List());
  for(k=1, n^2,
    if(issquare(n^2+k^2-k, &d) && d!=n,
      listput(L, d)
    )
  );
  Vec(L)
}
vector(100, n, n++; ceviso(n)[1])

Crossrefs

Cf. A264263.

Sequence in context: A094243 A155875 A105274 * A089390 A053667 A218072

Adjacent sequences: A264261 A264262 A264263 * A264265 A264266 A264267

Keyword

nonn,easy

Author

Colin Barker, Nov 10 2015

Status

approved